This invention relates to a method and an apparatus for designing roads, and more particularly to, a method and an apparatus for designing roads which enable to generate clothoid curves without executing exceptional processing near clothoid origins, in case of generating curvature transition curves of the roads using the clothoid curves.
In order to design roads, not only line segments and circular arcs but also curves, that is curvature transition curves, for linking the line segments and the circular arcs, which are inserted at the point where curvatures vary, are required. It is regulated to use the curvature transition curves on highly standardized roads such as express highways by the road structure ordinance. Clothoid curves are usually used as the curvature transition curves.
A clothoid curve (Cornu Spiral) is a curve whose curvature is directly proportional to its arc length. The curve, which has a peculiar characteristic, is employed in linking circular arcs together, line segments together, and a circular arc and a line segment from of old. And recently, the clothoid curve is generated by using a computer such as a personal computer.
In the conventional method for designing roads using clothoid curves which are generated by using a computer such as a personal computer, however, there are disadvantages in that exceptional processing is required for calculating coordinates (X, Y) near a clothoid origin, the calculation of an intersection of lines (roads) can not be executed in case the intersection of the lines (the roads) comes to near a clothoid origin, and the calculation of the shortest distance (the length of a perpendicular line) from a road centerline to an arbitrary point can not be executed in case the perpendicular line passes near a clothoid origin, because in case of calculating the coordinates (X, Y) near the clothoid origin, the calculation results become indefinite, that is to say, the coordinates near the clothoid origin can not be calculated
And more, the exceptional processing causes slow execution speed and complicated processing, and obstructs unified processing by using parameters, the real length of which compound curves are used as roads.
Moreover, in case the calculation of the shortest distance can not be executed, the road design can not be executed easily.
Accordingly, it is an object of the invention to provide a method and an apparatus for designing roads, which enable to generate clothoid curves without executing exceptional processing near clothoid origins, in case of generating curvature transition curves of the roads using the clothoid curves.
According to the first feature of the invention, an apparatus for designing roads, which is an apparatus for designing roads using line segments, circular arcs, clothoid curves and so on, comprises input means for inputting information of design conditions and/or a command of design processing and so on, design conditions storage means for storing the information of the design conditions input by the input means, road design processing means for executing road design in accordance with the command of the design processing input by the input means and/or the information of the design conditions stored in the design conditions storage means and for generating a road design map, and output means for outputting the road design map generated by the road design processing means, wherein the road design processing means generates a clothoid curve from a clothoid origin without executing exceptional processing near the clothoid origin in case of generating a curvature transition curve of the road using the clothoid curve, by calculating coordinates of the clothoid curve using the following recurrence equation (1), of which parameters are only the arc length xe2x80x9clxe2x80x9d from the clothoid origin, expressed as                                                         x              =                                                ∑                                      n                    =                    0                                    ∞                                ⁢                                                                            (                                              -                        1                                            )                                        n                                    ⁢                                                            l                                                                        4                          ⁢                          n                                                +                        1                                                                                                            (                                                                              4                            ⁢                            n                                                    +                          1                                                )                                            ·                                              2                                                  2                          ⁢                          n                                                                    ·                                                                        (                                                      2                            ⁢                            n                                                    )                                                !                                                                                                                                                                    y              =                                                ∑                                      n                    =                    0                                    ∞                                ⁢                                                                            (                                              -                        1                                            )                                        n                                    ⁢                                                            l                                                                        4                          ⁢                          n                                                +                        3                                                                                                            (                                                                              4                            ⁢                            n                                                    +                          3                                                )                                            ·                                              2                                                                              2                            ⁢                            n                                                    +                          1                                                                    ·                                                                        (                                                                                    2                              ⁢                              n                                                        +                            1                                                    )                                                !                                                                                                                                                    (                  Equation          ⁢                      xe2x80x83                    ⁢          1                )            
where xe2x80x9clxe2x80x9d is the unit clothoid arc length, xe2x80x9cxxe2x80x9d and xe2x80x9cyxe2x80x9d is the coordinate of the arc length xe2x80x9cl xe2x80x9d from the clothoid origin of the unit clothoid curve, and xe2x80x9cnxe2x80x9d is order.
According to the second feature of the invention, an apparatus for designing roads, which is an apparatus for designing roads using line segments, circular arcs, clothoid curves and so on, comprises input means for inputting information of design conditions and/or a command of design processing and so on, design conditions storage means for storing the information of the design conditions input by the input means, road design processing means for executing road design in accordance with the command of the design processing input by the input means and/or the information of the design conditions stored in the design conditions storage means and for generating a road design map, result storage means for storing the road design map generated by the road design processing means, and output means for outputting the road design map stored by the result storage means, wherein the road design processing means generates a clothoid curve from a clothoid origin without executing exceptional processing near the clothoid origin in case of generating a curvature transition curve of the road using the clothoid curve, by calculating coordinates of the clothoid curve using the following recurrence equation (1), of which parameters are only the arc length xe2x80x9clxe2x80x9d from the clothoid origin, expressed as                                                         x              =                                                ∑                                      n                    =                    0                                    ∞                                ⁢                                                                            (                                              -                        1                                            )                                        n                                    ⁢                                                            l                                                                        4                          ⁢                          n                                                +                        1                                                                                                            (                                                                              4                            ⁢                            n                                                    +                          1                                                )                                            ·                                              2                                                  2                          ⁢                          n                                                                    ·                                                                        (                                                      2                            ⁢                            n                                                    )                                                !                                                                                                                                                                    y              =                                                ∑                                      n                    =                    0                                    ∞                                ⁢                                                                            (                                              -                        1                                            )                                        n                                    ⁢                                                            l                                                                        4                          ⁢                          n                                                +                        3                                                                                                            (                                                                              4                            ⁢                            n                                                    +                          3                                                )                                            ·                                              2                                                                              2                            ⁢                            n                                                    +                          1                                                                    ·                                                                        (                                                                                    2                              ⁢                              n                                                        +                            1                                                    )                                                !                                                                                                                                                    (                  Equation          ⁢                      xe2x80x83                    ⁢          1                )            
where xe2x80x9clxe2x80x9d is the unit clothoid arc length, xe2x80x9cxxe2x80x9d and xe2x80x9cyxe2x80x9d is the coordinate of the arc length xe2x80x9clxe2x80x9d from the clothoid origin of the unit clothoid curve, and xe2x80x9cnxe2x80x9d is order.
According to the third feature of the invention, an apparatus for designing roads comprises road design processing means for generating a clothoid curve using the following relation equation (2) of a xe2x80x9cnxe2x80x9d term (Tx(n), Ty(n)), which is deduced by expanding xe2x80x9cxxe2x80x9d and xe2x80x9cyxe2x80x9d of the recurrence equation (1) in a series, expressed as                                                                         Tx                ⁡                                  (                                      n                    +                    1                                    )                                            =                                                -                                                                                    (                                                                              4                            ⁢                            n                                                    +                          1                                                )                                            ·                                              l                        4                                                                                    4                      ·                                              (                                                                              4                            ⁢                            n                                                    +                          5                                                )                                            ·                                              (                                                                              2                            ⁢                            n                                                    +                          2                                                )                                            ·                                              (                                                                              2                            ⁢                            n                                                    +                          1                                                )                                                                                            ⁢                                  Tx                  ⁡                                      (                    n                    )                                                                                                                                          xe2x80x83                            ⁢                              (                                                      n                    =                    0                                    ,                  1                  ,                  2                  ,                  …                                )                                                                                                        Tx                ⁡                                  (                  0                  )                                            =              l                                                                                          Ty                ⁡                                  (                                      n                    +                    1                                    )                                            =                                                -                                                                                    (                                                                              4                            ⁢                            n                                                    +                          3                                                )                                            ·                                              l                        4                                                                                    4                      ·                                              (                                                                              4                            ⁢                            n                                                    +                          7                                                )                                            ·                                              (                                                                              2                            ⁢                            n                                                    +                          3                                                )                                            ·                                              (                                                                              2                            ⁢                            n                                                    +                          2                                                )                                                                                            ⁢                                  Ty                  ⁡                                      (                    n                    )                                                                                                                                          xe2x80x83                            ⁢                              (                                                      n                    =                    0                                    ,                  1                  ,                  2                  ,                  …                                )                                                                                                        Ty                ⁡                                  (                  0                  )                                            =                                                l                  3                                                  3                  ·                  2                                                                                        (                  Equation          ⁢                      xe2x80x83                    ⁢          2                )            
According to the forth feature of the invention, a method for designing roads comprises the steps of (A) storing input information of design conditions, (B) executing road design in accordance with an input command of design processing and/or the stored information of the design conditions and generating a road design map using line segments, circular arcs, clothoid curves and so on, and (C) outputting the generated road design map, wherein the step (B) carries out generating a clothoid curve from a clothoid origin without executing exceptional processing near the clothoid origin in case of generating a curvature transition curve of the road using the clothoid curve, by calculating coordinates of the clothoid curve using the following recurrence equation (1), of which parameters are only the arc length xe2x80x9clxe2x80x9d from the clothoid origin expressed as                                                         x              =                                                ∑                                      n                    =                    0                                    ∞                                ⁢                                                                            (                                              -                        1                                            )                                        n                                    ⁢                                                            l                                                                        4                          ⁢                          n                                                +                        1                                                                                                            (                                                                              4                            ⁢                            n                                                    +                          1                                                )                                            ·                                              2                                                  2                          ⁢                          n                                                                    ·                                                                        (                                                      2                            ⁢                            n                                                    )                                                !                                                                                                                                                                    y              =                                                ∑                                      n                    =                    0                                    ∞                                ⁢                                                                            (                                              -                        1                                            )                                        n                                    ⁢                                                            l                                                                        4                          ⁢                          n                                                +                        3                                                                                                            (                                                                              4                            ⁢                            n                                                    +                          3                                                )                                            ·                                              2                                                                              2                            ⁢                            n                                                    +                          1                                                                    ·                                                                        (                                                                                    2                              ⁢                              n                                                        +                            1                                                    )                                                !                                                                                                                                                    (                  Equation          ⁢                      xe2x80x83                    ⁢          1                )            
where xe2x80x9clxe2x80x9d is the unit clothoid arc length, xe2x80x9cxxe2x80x9d and xe2x80x9cyxe2x80x9d is the coordinate of the arc length xe2x80x9cl xe2x80x9d from the clothoid origin of the unit clothoid curve, and xe2x80x9cnxe2x80x9d is order.
According to the fifth feature of the invention, a method for designing roads comprises the steps of (A) storing input information of design conditions, (B) executing road design in accordance with an input command of design processing and/or the stored information of the design conditions and generating a road design map using line segments, circular arcs, clothoid curves and so on, (C) storing the generated road design map, and (D) outputting the stored road design map, wherein the step (B) carries out generating a clothoid curve from a clothoid origin without executing exceptional processing near the clothoid origin in case of generating a curvature transition curve of the road using the clothoid curve, by calculating coordinates of the clothoid curve using the following recurrence equation (1), of which parameters are only the arc length xe2x80x9clxe2x80x9d from the clothoid origin, expressed as                                                         x              =                                                ∑                                      n                    =                    0                                    ∞                                ⁢                                                                            (                                              -                        1                                            )                                        n                                    ⁢                                                            l                                                                        4                          ⁢                          n                                                +                        1                                                                                                            (                                                                              4                            ⁢                            n                                                    +                          1                                                )                                            ·                                              2                                                  2                          ⁢                          n                                                                    ·                                                                        (                                                      2                            ⁢                            n                                                    )                                                !                                                                                                                                                                    y              =                                                ∑                                      n                    =                    0                                    ∞                                ⁢                                                                            (                                              -                        1                                            )                                        n                                    ⁢                                                            l                                                                        4                          ⁢                          n                                                +                        3                                                                                                            (                                                                              4                            ⁢                            n                                                    +                          3                                                )                                            ·                                              2                                                                              2                            ⁢                            n                                                    +                          1                                                                    ·                                                                        (                                                                                    2                              ⁢                              n                                                        +                            1                                                    )                                                !                                                                                                                                                    (                  Equation          ⁢                      xe2x80x83                    ⁢          1                )            
where xe2x80x9clxe2x80x9d is the unit clothoid arc length, xe2x80x9cxxe2x80x9d and xe2x80x9cyxe2x80x9d is the coordinate of the arc length xe2x80x9clxe2x80x9d from the clothoid origin of the unit clothoid curve, and xe2x80x9cnxe2x80x9d is order.
According to the sixth feature of the invention, a method for designing roads comprises the step of (B) generating a clothoid curve using the following relation equation (2) of a xe2x80x9cnxe2x80x9d term (Tx(n), Ty(n)), which is deduced by expanding xe2x80x9cxxe2x80x9d and xe2x80x9cyxe2x80x9d of the recurrence equation (1) in a series, expressed as                                                                         Tx                ⁡                                  (                                      n                    +                    1                                    )                                            =                                                -                                                                                    (                                                                              4                            ⁢                            n                                                    +                          1                                                )                                            ·                                              l                        4                                                                                    4                      ·                                              (                                                                              4                            ⁢                            n                                                    +                          5                                                )                                            ·                                              (                                                                              2                            ⁢                            n                                                    +                          2                                                )                                            ·                                              (                                                                              2                            ⁢                            n                                                    +                          1                                                )                                                                                            ⁢                                  Tx                  ⁡                                      (                    n                    )                                                                                                                                          xe2x80x83                            ⁢                              (                                                      n                    =                    0                                    ,                  1                  ,                  2                  ,                  …                                )                                                                                                        Tx                ⁡                                  (                  0                  )                                            =              l                                                                                          Ty                ⁡                                  (                                      n                    +                    1                                    )                                            =                                                -                                                                                    (                                                                              4                            ⁢                            n                                                    +                          3                                                )                                            ·                                              l                        4                                                                                    4                      ·                                              (                                                                              4                            ⁢                            n                                                    +                          7                                                )                                            ·                                              (                                                                              2                            ⁢                            n                                                    +                          3                                                )                                            ·                                              (                                                                              2                            ⁢                            n                                                    +                          2                                                )                                                                                            ⁢                                  Ty                  ⁡                                      (                    n                    )                                                                                                                                          xe2x80x83                            ⁢                              (                                                      n                    =                    0                                    ,                  1                  ,                  2                  ,                  …                                )                                                                                                        Ty                ⁡                                  (                  0                  )                                            =                                                l                  3                                                  3                  ·                  2                                                                                        (                  Equation          ⁢                      xe2x80x83                    ⁢          2                )            
According to the seventh feature of the invention, program products for designing roads, which is executed by computer system, comprises the steps of (A) storing input information of design conditions, (B) executing road design in accordance with an input command of design processing and/or the stored information of the design conditions and generating a road design map using line segments, circular arcs, clothoid curves and so on, and (C) outputting the generated road design map, wherein the step (B) carries out generating a clothoid curve from a clothoid origin without executing exceptional processing near the clothoid origin in case of generating a curvature transition curve of the road using the clothoid curve, by calculating coordinates of the clothoid curve using the following recurrence equation (1), of which parameters are only the arc length xe2x80x9clxe2x80x9d from the clothoid origin, expressed as                                                         x              =                                                ∑                                      n                    =                    0                                    ∞                                ⁢                                                                            (                                              -                        1                                            )                                        n                                    ⁢                                                            l                                                                        4                          ⁢                          n                                                +                        1                                                                                                            (                                                                              4                            ⁢                            n                                                    +                          1                                                )                                            ·                                              2                                                  2                          ⁢                          n                                                                    ·                                                                        (                                                      2                            ⁢                            n                                                    )                                                !                                                                                                                                                                    y              =                                                ∑                                      n                    =                    0                                    ∞                                ⁢                                                                            (                                              -                        1                                            )                                        n                                    ⁢                                                            l                                                                        4                          ⁢                          n                                                +                        3                                                                                                            (                                                                              4                            ⁢                            n                                                    +                          3                                                )                                            ·                                              2                                                                              2                            ⁢                            n                                                    +                          1                                                                    ·                                                                        (                                                                                    2                              ⁢                              n                                                        +                            1                                                    )                                                !                                                                                                                                                    (                  Equation          ⁢                      xe2x80x83                    ⁢          1                )            
where xe2x80x9clxe2x80x9d is the unit clothoid arc length, xe2x80x9cxxe2x80x9d and xe2x80x9cyxe2x80x9d is the coordinate of the arc length xe2x80x9clxe2x80x9d from the clothoid origin of the unit clothoid curve, and xe2x80x9cnxe2x80x9d is order.
According to the eighth feature of the invention, program products for designing roads, which is executed by computer system, comprises the steps of (A) storing input information of design conditions, (B) executing road design in accordance with an input command of design processing and/or the stored information of the design conditions and generating a road design map using line segments, circular arcs, clothoid curves and so on, (C) storing the generated road design map, and (D) outputting the stored road design map, wherein the step (B) carries out generating a clothoid curve from a clothoid origin without executing exceptional processing near the clothoid origin in case of generating a curvature transition curve of the road using the clothoid curve, by calculating coordinates of the clothoid curve using the following recurrence equation (1), of which parameters are only the arc length xe2x80x9clxe2x80x9d from the clothoid origin, expressed as                                                         x              =                                                ∑                                      n                    =                    0                                    ∞                                ⁢                                                                            (                                              -                        1                                            )                                        n                                    ⁢                                                            l                                                                        4                          ⁢                          n                                                +                        1                                                                                                            (                                                                              4                            ⁢                            n                                                    +                          1                                                )                                            ·                                              2                                                  2                          ⁢                          n                                                                    ·                                                                        (                                                      2                            ⁢                            n                                                    )                                                !                                                                                                                                                                    y              =                                                ∑                                      n                    =                    0                                    ∞                                ⁢                                                                            (                                              -                        1                                            )                                        n                                    ⁢                                                            l                                                                        4                          ⁢                          n                                                +                        3                                                                                                            (                                                                              4                            ⁢                            n                                                    +                          3                                                )                                            ·                                              2                                                                              2                            ⁢                            n                                                    +                          1                                                                    ·                                                                        (                                                                                    2                              ⁢                              n                                                        +                            1                                                    )                                                !                                                                                                                                                    (                  Equation          ⁢                      xe2x80x83                    ⁢          1                )            
where xe2x80x9clxe2x80x9d is the unit clothoid arc length, xe2x80x9cxxe2x80x9d and xe2x80x9cyxe2x80x9d is the coordinate of the arc length xe2x80x9clxe2x80x9d from the clothoid origin of the unit clothoid curve, and xe2x80x9cnxe2x80x9d is order.
According to the ninth feature of the invention, program products for designing roads comprises the step of (B) generating a clothoid curve using the following relation equation (2) of a xe2x80x9cnxe2x80x9d term (Tx(n), Ty(n)), which is deduced by expanding xe2x80x9cxxe2x80x9d and xe2x80x9cyxe2x80x9d of the recurrence equation (1) in a series, expressed as                                                                         Tx                ⁡                                  (                                      n                    +                    1                                    )                                            =                                                -                                                                                    (                                                                              4                            ⁢                            n                                                    +                          1                                                )                                            ·                                              l                        4                                                                                    4                      ·                                              (                                                                              4                            ⁢                            n                                                    +                          5                                                )                                            ·                                              (                                                                              2                            ⁢                            n                                                    +                          2                                                )                                            ·                                              (                                                                              2                            ⁢                            n                                                    +                          1                                                )                                                                                            ⁢                                  Tx                  ⁡                                      (                    n                    )                                                                                                                                          xe2x80x83                            ⁢                              (                                                      n                    =                    0                                    ,                  1                  ,                  2                  ,                  …                                )                                                                                                        Tx                ⁡                                  (                  0                  )                                            =              l                                                                                          Ty                ⁡                                  (                                      n                    +                    1                                    )                                            =                                                -                                                                                    (                                                                              4                            ⁢                            n                                                    +                          3                                                )                                            ·                                              l                        4                                                                                    4                      ·                                              (                                                                              4                            ⁢                            n                                                    +                          7                                                )                                            ·                                              (                                                                              2                            ⁢                            n                                                    +                          3                                                )                                            ·                                              (                                                                              2                            ⁢                            n                                                    +                          2                                                )                                                                                            ⁢                                  Ty                  ⁡                                      (                    n                    )                                                                                                                                          xe2x80x83                            ⁢                              (                                                      n                    =                    0                                    ,                  1                  ,                  2                  ,                  …                                )                                                                                                        Ty                ⁡                                  (                  0                  )                                            =                                                l                  3                                                  3                  ·                  2                                                                                        (                  Equation          ⁢                      xe2x80x83                    ⁢          2                )            